Yes, honey is very popular. Bumthang honey from around the Jakar area is very famous.
The butterflies were amazing! I saw them mostly in the east but it could just have had to do with the climate and time of year. I think there are probably more butterflies in the warmer months of summer.
Not sure about the king and queen. But I have the impression that he is very down to earth. Whenever there is a natural disaster or fire he is always there to lend his moral support as well as some money to help the victims. So they may be out and about in Thimphu.